I usually just take the train or public bus. You can take any meter taxi from the airport to the train station and get a ride to phan thiet from there and then a meter taxi to Mui Ne proper. You will end up paying much less this way. The train leaves at 06:50 every day and arrives at 11:00. It is the SPT2 train. If you are getting harassed at the airport by taxis then turn right out of the international terminal and walk 200 meters to the domestic terminal. The taxis there are usually less aggressive and you can get a meter one. The ATMs tend to have smaller fees too. If you wish to take a bus then take a taxi to Pham Ngu Lao and go into any of the 300 travel agencies on the street. There are multiple departures every day and they drop you right off on the main drag of Mui Ne.

Thanks for information mate. My initial plan was to take the bus, but then I found out those Open Buses cost $18 one way. In that case, adding taxi fee to bus station, I would only pay like $25 more for a shared taxi straight from airport to Mui Ne beach guesthouse. No hassle with searching and waiting for a bus and getting around in Mui Ne. If I don`t find someone to share taxi with I will take the bus.